SOLUTION: Twelve girls try out for the hockey team. Two play goal, four play defence, and the rest play forward. How many different starting lineups could the coach choose if she needs 1 go

Algebra ->  Permutations -> SOLUTION: Twelve girls try out for the hockey team. Two play goal, four play defence, and the rest play forward. How many different starting lineups could the coach choose if she needs 1 go      Log On


   

Question 1183179: Twelve girls try out for the hockey team. Two play goal, four play defence, and the rest play forward. How many different starting lineups could the coach choose if she needs 1 goalie, 2 defence, and 3 forwards?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


To form a team, the coach needs to...

(1) choose 1 of the 2 goalies: C(2,1)
AND
(2) choose 2 of the 4 defenders: C(4,2)
AND
(3) choose 3 of the 6 forwards: C(6,3)

The number if possible starting lineups is the product of the numbers of ways he can choose the players for the three positions:

ANSWER: C%282%2C1%29%2AC%284%2C2%29%2AC%286%2C3%29+=+%282%29%286%29%2820%29+=+240